### hey. this is fun and easy.

$\sharp \{ (v_1, v_2, \ldots , v_k) \in (\{ j\}_{j=1}^{n})^k \mid [a \not= b] \Rightarrow [v_a \not= v_b]\}=$
${{n!}\over{(n-k)!}} = \null_n P_k.$
— the number of “permutations of k things
from a set of n” (“en-permute-kay”, in its
most convenient say-it-out-loud version);
the number of ways to make an (ordered)
*list* of k (distinct) things chosen from
a set of n things. one has known this from,
well, time immemorial. but never written
it out in straight-up *set* notation
until today.

now it’s on page 5 of my “bogart”.
(_introductory_combinatorics_, kenneth
p.~bogart, 1983; mine’s a recent acquisition
from the math complex, once of the
“bertha halley ross collection” according
to its bookplate. that turns out to have
been mrs. arnold ross, late of the OSU
[an all-time giant in recruiting new talent
into mathematics, founder of the “ross program”].
you can see from the edges of the pages that
somebody read it up to chapter six and stopped.
they didn’t write on the pages though.
[but that’s being put right now.])

and cranking out suchlike “set code” *is* fun
and easy… for me. showing somebody how to
*read* it? fun but *not* easy. showing some-
body how to *write* it? well… how would i
*know*? (how would *anyone*?)

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#### 2 Comments

1. http://www.math.dartmouth.edu/news-resources/electronic/kpbogart/

combinatorics through guided discovery
(free download PDF).

2. maybe *now* the code’s right…

• ## (Partial) Contents Page

Vlorbik On Math Ed ('07—'09)
(a good place to start!)